2007 Lecture Notes and Notebooks:The first column contains pdf with hyperlinks and
is best if you are going to read the lecture on a computer screen; the other pdfs are intended for
those who print. The Notebook contains an (unevaluated) Mathematica (6.0) notebook that goes with the
lecture. The final column is html of the evaluated notebook. Animations will not be visible in the html

Fourier Transforms and its Interpretation, Extension of Fourier Series to Infinite Wavelength,
Higher dimensional Fourier Transforms, Transforms of Delta-Functions, Convolution Theorem
Functional Basis, Functional Orthogonality, Complex Form of the Fourier Series

Simulated Diffraction and Selected Area Diffraction from Simulated Atomic Scatters, Polycrystals,
and Lattices with Thermal Vibrations.

General Solutions to General Linear Homogeneous and Heterogeneous First-Order ODEs, Transformation
of Variables in ODEs, Numerical Solutions to Nonlinear First-Order ODEs, Extracting Solutions for
Visualization from Numerical Solutions to ODEs.

Explicit Second-Order Differencing and its Visualization, Deriving Solutions to
2nd Order ODEs with constant coefficients, Building Up Graphics to Characterize
Solution Behavior in terms of Constant Coefficients,
Solving for Boundary Conditions, General Solutions to the Beam Equation for Common
Loading and Boundary Condtions, Visualization of Beam Deflections, a Gratiutous Example
of an Interactive Beam Equation Solver.

The general public is free to use these notes for
educational purposes. Complete sets can be made available, please
contact ccarter@mit.edu---and
please if you copy these notes and distribute them in any way, please
attribute properly. If you use these notes, please attribute the
author; I would very much
appreciate your comments, both positive and negative, about
these notes. ---WCC